18CS3070 OT 9/8/23

Q1. A farmer has 2400 m of fencing off a rectangular field that borders a straight river. He needs no fence along the river. Predict the dimensions of the field that has the largest area.

• x=1200, y=600

• x=2200, y=100

• x=1600, y=400

• x=1200, y=1200

Q2. Thumb rule for designing variables in an optimization problem is.   

• To choose only one design variables

   

• To choose only two design variables

   

• To choose a few design variables

• To choose more design variables

   

Q3. Define surplus variable.

• It is a variable which is added to a constraint to turn the equality constraint into an equation

• It is a variable which is subtracted from a constraint to turn the equality constraint into an equation

• It is a variable which is added to a constraint to turn the inequality into an equation

• It is a variable which is subtracted from a constraint to turn the inequality into an equation

Q4. Identify the types of constraints in Linear Programming model

• 4

• 2

• 1

• 3

Q5. Convert the following inequality constraint into an equal constraint

10x+30y≤4000

• 10x+30y+s₁ = 4000, where s₁ is slack variable

• 10x+30y-s₁ = 4000, where s₁ is slack variable

• 10x+30y+s₁ = 4000, where s₁ is surplus variable

• 10x+30y+s₁ = 4000, where s₁ is decision variable